Nuprl Lemma : atom_eq_sq_normalize
∀[b1,b2,i,j:Top]. (if i=j then b1[i] else b2 fi ~ if i=j then b1[j] else b2 fi )
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
atom_eq: if a=b then c else d fi ,
sqequal: s ~ t
Definitions unfolded in proof :
so_apply: x[s],
has-value: (a)↓,
member: t ∈ T,
and: P ∧ Q,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
sq_type: SQType(T),
implies: P ⇒ Q,
guard: {T},
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
assert: ↑b,
false: False,
iff: P ⇐⇒ Q,
not: ¬A,
rev_implies: P ⇐ Q
Lemmas referenced :
decidable__atom_equal,
subtype_base_sq,
atom_subtype_base,
eq_atom_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_atom,
has-value_wf_base,
is-exception_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
bool_subtype_base,
iff_transitivity,
assert_wf,
bnot_wf,
not_wf,
equal-wf-base,
iff_weakening_uiff,
assert_of_bnot,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
sqequalRule,
thin,
sqequalSqle,
divergentSqle,
callbyvalueAtomEq,
sqequalHypSubstitution,
hypothesis,
baseApply,
closedConclusion,
baseClosed,
hypothesisEquality,
productElimination,
introduction,
extract_by_obid,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
unionElimination,
instantiate,
isectElimination,
cumulativity,
atomEquality,
independent_isectElimination,
independent_functionElimination,
lambdaFormation,
equalityElimination,
because_Cache,
atom_eqReduceTrueSq,
sqleReflexivity,
dependent_pairFormation,
promote_hyp,
voidElimination,
independent_pairFormation,
impliesFunctionality,
atom_eqReduceFalseSq,
atom_eqExceptionCases,
axiomSqleEquality,
exceptionSqequal,
isect_memberFormation,
sqequalAxiom,
isect_memberEquality,
exceptionAtomeq
Latex:
\mforall{}[b1,b2,i,j:Top]. (if i=j then b1[i] else b2 fi \msim{} if i=j then b1[j] else b2 fi )
Date html generated:
2017_04_14-AM-07_22_12
Last ObjectModification:
2017_02_27-PM-02_55_18
Theory : call!by!value_2
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