Nuprl Rule : lessExceptionCases

This rule proved as lemma rule_less_exception_cases_true in file rules/rules_less_exception.v
at https://github.com/vrahli/NuprlInCoq

H  ⊢ a = b ∈ T

  BY lessExceptionCases x y t u z w ()

  H  ⊢ is-exception(if (t) < (u)  then z  else w)
  H x:(t ∈ ℤ), y:(u ∈ ℤ) ⊢ a = b ∈ T
  H x:(t ∈ ℤ), y:is-exception(u) ⊢ a = b ∈ T
  H x:is-exception(t) ⊢ a = b ∈ T
  H  ⊢ t ∈ Base
  H  ⊢ u ∈ Base

Definitions occuring in rule : less: if (a) < (b) then c else d, int: ℤ, is-exception: is-exception(t), equal: s = t ∈ T, member: t ∈ T, base: Base, axiom: Ax

Latex:
H \mvdash{} a = b BY lessExceptionCases x y t u z w () H \mvdash{} is-exception(if (t) < (u) then z else w) H x:(t \mmember{} \mBbbZ{}), y:(u \mmember{} \mBbbZ{}) \mvdash{} a = b H x:(t \mmember{} \mBbbZ{}), y:is-exception(u) \mvdash{} a = b H x:is-exception(t) \mvdash{} a = b H \mvdash{} t \mmember{} Base H \mvdash{} u \mmember{} Base Date html generated: 2019_06_20-PM-04_12_04 Last ObjectModification: 2016_07_08-PM-03_48_51 Theory : rules Home Index