Nuprl Lemma : tswap_wf
∀n:ℕ. ∀i,j:ℕn. (swap{n}(i;j) ∈ ℕn ⟶ ℕn)
Proof
Definitions occuring in Statement :
tswap: swap{n}(i;j),
int_seg: {i..j-},
nat: ℕ,
all: ∀x:A. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
tswap: swap{n}(i;j),
uall: ∀[x:A]. B[x],
nat: ℕ
Lemmas referenced :
swap_wf,
int_seg_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
sqequalRule,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis,
inhabitedIsType,
universeIsType,
isectElimination,
natural_numberEquality,
setElimination,
rename
Latex:
\mforall{}n:\mBbbN{}. \mforall{}i,j:\mBbbN{}n. (swap\{n\}(i;j) \mmember{} \mBbbN{}n {}\mrightarrow{} \mBbbN{}n)
Date html generated:
2019_10_16-PM-00_59_11
Last ObjectModification:
2018_10_08-AM-09_46_28
Theory : perms_1
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