Nuprl Lemma : comb_for_extend_permf_wf
λn,p,z. extend_permf(p;n) ∈ n:ℕ ⟶ p:(ℕn ⟶ ℕn) ⟶ (↓True) ⟶ ℕn + 1 ⟶ ℕn + 1
Proof
Definitions occuring in Statement :
extend_permf: extend_permf(pf;n),
int_seg: {i..j-},
nat: ℕ,
squash: ↓T,
true: True,
member: t ∈ T,
lambda: λx.A[x],
function: x:A ⟶ B[x],
add: n + m,
natural_number: $n
Definitions unfolded in proof :
member: t ∈ T,
squash: ↓T,
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
prop: ℙ,
nat: ℕ
Lemmas referenced :
extend_permf_wf,
squash_wf,
true_wf,
int_seg_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaEquality_alt,
sqequalHypSubstitution,
imageElimination,
cut,
introduction,
extract_by_obid,
dependent_functionElimination,
thin,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
universeIsType,
isectElimination,
functionIsType,
natural_numberEquality,
setElimination,
rename,
inhabitedIsType
Latex:
\mlambda{}n,p,z. extend\_permf(p;n) \mmember{} n:\mBbbN{} {}\mrightarrow{} p:(\mBbbN{}n {}\mrightarrow{} \mBbbN{}n) {}\mrightarrow{} (\mdownarrow{}True) {}\mrightarrow{} \mBbbN{}n + 1 {}\mrightarrow{} \mBbbN{}n + 1
Date html generated:
2019_10_16-PM-00_59_49
Last ObjectModification:
2018_10_08-AM-09_20_23
Theory : perms_1
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