Nuprl Lemma : nat-id-fun-ext
∀n:ℕ. (∃m:ℕ [(m = n ∈ ℕ)])
Proof
Definitions occuring in Statement :
nat: ℕ,
all: ∀x:A. B[x],
sq_exists: ∃x:A [B[x]],
equal: s = t ∈ T
Definitions unfolded in proof :
member: t ∈ T,
nat-id-fun-example,
any: any x,
decidable__equal_int,
decidable__int_equal,
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],
so_lambda: λ2x.t[x],
top: Top,
so_apply: x[s],
uimplies: b supposing a,
strict4: strict4(F),
and: P ∧ Q,
all: ∀x:A. B[x],
implies: P ⇒ Q,
has-value: (a)↓,
prop: ℙ,
guard: {T},
or: P ∨ Q,
squash: ↓T,
subtract: n - m,
int_seg_properties
Lemmas referenced :
nat-id-fun-example,
lifting-strict-int_eq,
top_wf,
equal_wf,
has-value_wf_base,
base_wf,
is-exception_wf,
decidable__equal_int,
decidable__int_equal,
int_seg_properties
Rules used in proof :
introduction,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
instantiate,
extract_by_obid,
hypothesis,
sqequalRule,
thin,
sqequalHypSubstitution,
isectElimination,
baseClosed,
isect_memberEquality,
voidElimination,
voidEquality,
independent_isectElimination,
independent_pairFormation,
lambdaFormation,
callbyvalueDecide,
hypothesisEquality,
equalityTransitivity,
equalitySymmetry,
unionEquality,
unionElimination,
sqleReflexivity,
dependent_functionElimination,
independent_functionElimination,
baseApply,
closedConclusion,
decideExceptionCases,
inrFormation,
because_Cache,
imageMemberEquality,
imageElimination,
exceptionSqequal,
inlFormation
Latex:
\mforall{}n:\mBbbN{}. (\mexists{}m:\mBbbN{} [(m = n)])
Date html generated:
2018_05_21-PM-11_39_15
Last ObjectModification:
2017_07_26-PM-06_42_47
Theory : rationals
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