Nuprl Lemma : lifting-strict-int_eq
∀[F:Base]. ∀[p,q,r:Top].
  ∀[a,b,c,d:Top].  (F[if a=b then c else d;p;q;r] ~ if a=b then F[c;p;q;r] else F[d;p;q;r]) 
  supposing strict4(λx,y,z,w. F[x;y;z;w])
Proof
Definitions occuring in Statement : 
strict4: strict4(F)
, 
uimplies: b supposing a
, 
uall: ∀[x:A]. B[x]
, 
top: Top
, 
so_apply: x[s1;s2;s3;s4]
, 
int_eq: if a=b then c else d
, 
lambda: λx.A[x]
, 
base: Base
, 
sqequal: s ~ t
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
uimplies: b supposing a
, 
strict4: strict4(F)
, 
and: P ∧ Q
, 
cand: A c∧ B
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
has-value: (a)↓
, 
bool: 𝔹
, 
unit: Unit
, 
it: ⋅
, 
btrue: tt
, 
uiff: uiff(P;Q)
, 
bfalse: ff
, 
exists: ∃x:A. B[x]
, 
or: P ∨ Q
, 
sq_type: SQType(T)
, 
guard: {T}
, 
bnot: ¬bb
, 
ifthenelse: if b then t else f fi 
, 
assert: ↑b
, 
false: False
, 
iff: P 
⇐⇒ Q
, 
not: ¬A
, 
rev_implies: P 
⇐ Q
, 
prop: ℙ
, 
squash: ↓T
, 
so_apply: x[s1;s2;s3;s4]
Lemmas referenced : 
eq_int_wf, 
eqtt_to_assert, 
assert_of_eq_int, 
has-value_wf_base, 
is-exception_wf, 
eqff_to_assert, 
bool_cases_sqequal, 
subtype_base_sq, 
bool_wf, 
bool_subtype_base, 
iff_transitivity, 
assert_wf, 
bnot_wf, 
not_wf, 
equal-wf-base, 
iff_weakening_uiff, 
assert_of_bnot, 
strict4_wf, 
top_wf, 
base_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
Error :isect_memberFormation_alt, 
introduction, 
cut, 
sqequalSqle, 
sqleRule, 
thin, 
divergentSqle, 
sqequalHypSubstitution, 
sqequalRule, 
productElimination, 
hypothesis, 
dependent_functionElimination, 
baseApply, 
closedConclusion, 
baseClosed, 
hypothesisEquality, 
independent_functionElimination, 
callbyvalueIntEq, 
extract_by_obid, 
isectElimination, 
Error :inhabitedIsType, 
Error :lambdaFormation_alt, 
unionElimination, 
equalityElimination, 
because_Cache, 
independent_isectElimination, 
equalityTransitivity, 
equalitySymmetry, 
int_eqReduceTrueSq, 
sqleReflexivity, 
Error :dependent_pairFormation_alt, 
Error :equalityIsType2, 
promote_hyp, 
instantiate, 
cumulativity, 
voidElimination, 
intEquality, 
independent_pairFormation, 
Error :equalityIsType4, 
Error :universeIsType, 
int_eqReduceFalseSq, 
Error :equalityIsType1, 
imageElimination, 
axiomSqleEquality, 
int_eqExceptionCases, 
exceptionSqequal, 
axiomSqEquality, 
Error :isect_memberEquality_alt, 
exceptionInteq
Latex:
\mforall{}[F:Base].  \mforall{}[p,q,r:Top].
    \mforall{}[a,b,c,d:Top].    (F[if  a=b  then  c  else  d;p;q;r]  \msim{}  if  a=b  then  F[c;p;q;r]  else  F[d;p;q;r]) 
    supposing  strict4(\mlambda{}x,y,z,w.  F[x;y;z;w])
Date html generated:
2019_06_20-AM-11_27_11
Last ObjectModification:
2018_09_28-PM-03_30_36
Theory : computation
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