Nuprl Lemma : mFOL-proveable-formula-evidence-ext2
Main Lemma. See mFOL-proveable-evidence also.⋅
∀[fmla:mFOL()]. (mFOL-proveable-formula(fmla) 
⇒ mFOL-evidence(fmla))
Proof
Definitions occuring in Statement : 
mFOL-proveable-formula: mFOL-proveable-formula(fmla)
, 
mFOL-evidence: mFOL-evidence(fmla)
, 
mFOL: mFOL()
, 
uall: ∀[x:A]. B[x]
, 
implies: P 
⇒ Q
Definitions unfolded in proof : 
member: t ∈ T
, 
eq_int: (i =z j)
, 
btrue: tt
, 
it: ⋅
, 
bfalse: ff
, 
band: p ∧b q
, 
ifthenelse: if b then t else f fi 
, 
bnot: ¬bb
, 
select-tuple: x.n
, 
pi1: fst(t)
, 
subtract: n - m
, 
pi2: snd(t)
, 
lt_int: i <z j
, 
le_int: i ≤z j
, 
genrec-ap: genrec-ap, 
spreadn: spread3, 
ifunion: ifunion(b; t)
, 
mFOL-proveable-formula-evidence-ext, 
uall: ∀[x:A]. B[x]
, 
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w])
, 
so_apply: x[s1;s2;s3;s4]
, 
top: Top
, 
uimplies: b supposing a
, 
strict4: strict4(F)
, 
and: P ∧ Q
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
has-value: (a)↓
, 
prop: ℙ
, 
or: P ∨ Q
, 
squash: ↓T
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
so_lambda: λ2x y.t[x; y]
, 
so_apply: x[s1;s2]
Lemmas referenced : 
mFOL-proveable-formula-evidence-ext, 
lifting-strict-decide, 
istype-void, 
has-value_wf_base, 
istype-base, 
is-exception_wf, 
istype-universe, 
lifting-strict-spread, 
strict4-spread, 
lifting-strict-atom_eq, 
strict4-decide, 
lifting-strict-int_eq, 
lifting-strict-less, 
value-type-has-value, 
int-value-type, 
lifting-strict-isaxiom
Rules used in proof : 
introduction, 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
cut, 
instantiate, 
extract_by_obid, 
hypothesis, 
sqequalRule, 
thin, 
sqequalHypSubstitution, 
equalityTransitivity, 
equalitySymmetry, 
isectElimination, 
baseClosed, 
isect_memberEquality_alt, 
voidElimination, 
independent_isectElimination, 
independent_pairFormation, 
lambdaFormation_alt, 
callbyvalueApply, 
universeIsType, 
baseApply, 
closedConclusion, 
hypothesisEquality, 
applyExceptionCases, 
inrFormation_alt, 
imageMemberEquality, 
imageElimination, 
inlFormation_alt, 
because_Cache, 
inhabitedIsType, 
sqequalSqle, 
divergentSqle, 
callbyvalueDecide, 
unionElimination, 
sqleReflexivity, 
equalityIsType1, 
dependent_functionElimination, 
independent_functionElimination, 
decideExceptionCases, 
axiomSqleEquality, 
exceptionSqequal, 
callbyvalueLess, 
productElimination, 
intEquality, 
lessExceptionCases, 
callbyvalueSpread, 
spreadExceptionCases
Latex:
\mforall{}[fmla:mFOL()].  (mFOL-proveable-formula(fmla)  {}\mRightarrow{}  mFOL-evidence(fmla))
Date html generated:
2019_10_16-AM-11_43_40
Last ObjectModification:
2018_10_12-AM-11_13_33
Theory : minimal-first-order-logic
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