Nuprl Lemma : comb_for_app_permf_wf
λm,n,p,q,z. app_permf(m;n;p;q) ∈ m:ℕ ⟶ n:ℕ ⟶ p:(ℕm ⟶ ℕm) ⟶ q:(ℕn ⟶ ℕn) ⟶ (↓True) ⟶ ℕm + n ⟶ ℕm + n
Proof
Definitions occuring in Statement :
app_permf: app_permf(m;n;p;q),
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 :
app_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{}m,n,p,q,z. app\_permf(m;n;p;q) \mmember{} m:\mBbbN{} {}\mrightarrow{} n:\mBbbN{} {}\mrightarrow{} p:(\mBbbN{}m {}\mrightarrow{} \mBbbN{}m) {}\mrightarrow{} q:(\mBbbN{}n {}\mrightarrow{} \mBbbN{}n) {}\mrightarrow{} (\mdownarrow{}True) {}\mrightarrow{} \mBbbN{}m + n {}\mrightarrow{} \000C\mBbbN{}m + n
Date html generated:
2019_10_16-PM-00_59_39
Last ObjectModification:
2018_10_08-AM-09_20_31
Theory : perms_1
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